You must be planning a nice long vacation!

Also check rome2rio.com, but be sure to click through to all the underlying web sites, as the main rome2rio pages aren't sensitive to seasonal variation in schedules.

Staying in beautiful Rovinj years ago we took a photo of the ferry that had just arrived from Venice. It has www.venezialines.com on the side of the vessel.

An option from Split to Venice is bus and train.

Google maps also shows a ferry from Bari to Dubrovnik. You could get the train from Rome to Bari.

Kay

If you are looking for most efficient/economical then probably flying in both cases. Definitely from Rome to Dubrovnik. Split to Venice could be just as efficient to take the ferry - just go to the respective websites to compare time and cost. If you were planning to be further north, in Istria (Rovinj) then ferry would probably win in terms of time over flying, and even from Split it might be. Bus/train would not be a good option unless you wanted to visit several places on the way (Istria/Rovin, Porec, etc., Piran or somewhere in Slovenia, Triest Italy).

"Ferry from Split to Venice" means
either
Overnight ferry from Split to Ancona plus train from Ancona to Riimini - (may be Bologna) - Ferrara - Padova - Venice
or
bus from Split to Zadar, ferry from Zadar to Mali Losinj or Pula, catamaran from Mali Losinj or Pula to Venice
Volotea has cheap flights between these 2 places

There used to be a Split-Venice ferry but if neckervd says no then no. Either take buses up the coast or trains via Zagreb or the ferry via Ancona. For lots on trains and booking own tickets check www.seat61.com; BETS-European Rail Experts and www.ricksteves.com. Of course flying Split-Venice is also viable and maybe best if in a hurry.

https://www.directferries.co.uk/venice_pula_ferry.htm

Not sure where Pula is but it's in Croatia and has ferries to Venice.

The daily Zadar - Mali Losinj - Pula - Venice ferry began to run some 100 years ago and stopped running some 25 years ago.
So did the Bar - Kotor - Dubrovnik - Korcula - Hvar town - Split - Sibenik - Zadar - Pula - Venice ferry (up to Venice only twice weekly during the season, daily to Rab - Rijeka and twice weekly to Pula - Trieste).

So there are no ferries Croatia to Venice? The Direct Ferries web site seems to be current and say Pula-Venice still running - but you say they stopped running 25 years ago?

There are almost daily ferries between Rovinj (and Pula) and Venice - one in each direction. That's according to the ferry website for this coming season (I think off season they are not as frequent). https://www.directferries.com/ferry/ I notice there is a ferry listed between Split and Anconia but not between Split and Venice.

" So there are no ferries Croatia to Venice? The Direct Ferries web site seems to be current and say Pula-Venice still running - but you say they stopped running 25 years ago?"
there is a misunderstanding:
The Zadar - Pula - Venice ferry (Italian domestic line until 1945, then international line operated by Yougoslavia) stopped to run in the early ninetees. It was then replaced by
a catamaran Trieste - Pula, operated initially by a company from Trieste, then by Usticalines Palermo which changed their name into Libertylines;
another catamaran Venice - Pula - Mali Losinj, operated by Venezialines;
ann finally the catamarans of the Istrian companies Atlas Kompas/Adriatic Line operating between Pula and Venice too.
The Italian company Gomo Viaggi operates furthermore catamarans from Cesenatico and Pesaro to Istria and Rab Island